The following result is a reformulation of [1]}.
It shows how Mihlin type estimates of a symbol \(a\)  are reflected by its distributional kernel \({\mathcal {F}}^{-1}a \in {\mathcal {S}}^{\prime }({\mathcal {L}}(X,Y))\) . Recall that \(\dot{\mathbb {R}}:=\mathbb {R}\setminus \lbrace 0\rbrace \) .
